Trailer sway is when the trailer starts to oscillate back and forth in ever increasing arcs. If it isn't brought under control, it eventually results in the destruction of the trailer and/or tow vehicle.
I have had one trailer (a home-built flatbed) that had a sway problem, and believe me, once you experience it you will never forget it! That trailer was so poorly built that there was no way to load it to stop the sway. I sold the horrible thing, and told the buyer about the problem, and what I thought had to be done to make it a decent trailer.
Wind wag or wind wander is something that one must learn to cope with, especially when towing longer trailers. It happens, no matter what kind of hitch is used. You will get used to it.